Write equation for the line in slope intercept form (6,4) and (3,8)

y = - 4x/3 + 12

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = y intercept

m represents the slope of the line.

m = (y2 - y1)/(x2 - x1)

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through (6, 4) and (3, 8),

y2 = 8

y1 = 4

x2 = 3

x1 = 6

Slope,m = (8 - 4)/(3 - 6) = 4/- 3 = - 4/3

To determine the y intercept, we would substitute x = 3, y = 8 and m= - 4/3 into y = mx + c. It becomes

8 = - 4/3 × 3 + c

8 = - 4 + c

c = 8 + 4

c = 12

The equation becomes

y = - 4x/3 + 12